seamless mesh placement
Ive had this issue before too and solved it like this:


Have the plane 2m x 2m in size
Apply the particle system
Join the particles to the plane
making it tile


(option 1)
 Duplicate the original plane and move it 2m to the left/right/top/bottom and corners 

(option2) use 2 array modifier, uncheck relative, check constant distance and set it to 2m on X and the other 2m on Y, now the middle one has all the overlapping parts.

that way the middle plane has all the overlapping parts

if you have multiple particle system, apply them all at the same time, join them together with the plane

Now you can proceed with the baking